56,006 research outputs found
Best Response Games on Regular Graphs
With the growth of the internet it is becoming increasingly important to
understand how the behaviour of players is affected by the topology of the
network interconnecting them. Many models which involve networks of interacting
players have been proposed and best response games are amongst the simplest. In
best response games each vertex simultaneously updates to employ the best
response to their current surroundings. We concentrate upon trying to
understand the dynamics of best response games on regular graphs with many
strategies. When more than two strategies are present highly complex dynamics
can ensue. We focus upon trying to understand exactly how best response games
on regular graphs sample from the space of possible cellular automata. To
understand this issue we investigate convex divisions in high dimensional space
and we prove that almost every division of dimensional space into
convex regions includes a single point where all regions meet. We then find
connections between the convex geometry of best response games and the theory
of alternating circuits on graphs. Exploiting these unexpected connections
allows us to gain an interesting answer to our question of when cellular
automata are best response games
On Rational Delegations in Liquid Democracy
Liquid democracy is a proxy voting method where proxies are delegable. We
propose and study a game-theoretic model of liquid democracy to address the
following question: when is it rational for a voter to delegate her vote? We
study the existence of pure-strategy Nash equilibria in this model, and how
group accuracy is affected by them. We complement these theoretical results by
means of agent-based simulations to study the effects of delegations on group's
accuracy on variously structured social networks.Comment: 17 pages, 3 figures. This paper (without Appendix) appears in the
proceedings of AAAI'1
Evolution of Coordination in Social Networks: A Numerical Study
Coordination games are important to explain efficient and desirable social
behavior. Here we study these games by extensive numerical simulation on
networked social structures using an evolutionary approach. We show that local
network effects may promote selection of efficient equilibria in both pure and
general coordination games and may explain social polarization. These results
are put into perspective with respect to known theoretical results. The main
insight we obtain is that clustering, and especially community structure in
social networks has a positive role in promoting socially efficient outcomes.Comment: preprint submitted to IJMP
The Max-Distance Network Creation Game on General Host Graphs
In this paper we study a generalization of the classic \emph{network creation
game} in the scenario in which the players sit on a given arbitrary
\emph{host graph}, which constrains the set of edges a player can activate at a
cost of each. This finds its motivations in the physical
limitations one can have in constructing links in practice, and it has been
studied in the past only when the routing cost component of a player is given
by the sum of distances to all the other nodes. Here, we focus on another
popular routing cost, namely that which takes into account for each player its
\emph{maximum} distance to any other player. For this version of the game, we
first analyze some of its computational and dynamic aspects, and then we
address the problem of understanding the structure of associated pure Nash
equilibria. In this respect, we show that the corresponding price of anarchy
(PoA) is fairly bad, even for several basic classes of host graphs. More
precisely, we first exhibit a lower bound of
for any . Notice that this implies a counter-intuitive lower
bound of for very small values of (i.e., edges can
be activated almost for free). Then, we show that when the host graph is
restricted to be either -regular (for any constant ), or a
2-dimensional grid, the PoA is still , which is proven to be tight for
. On the positive side, if , we show
the PoA is . Finally, in the case in which the host graph is very sparse
(i.e., , with ), we prove that the PoA is , for any
.Comment: 17 pages, 4 figure
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Statistical Mechanics of maximal independent sets
The graph theoretic concept of maximal independent set arises in several
practical problems in computer science as well as in game theory. A maximal
independent set is defined by the set of occupied nodes that satisfy some
packing and covering constraints. It is known that finding minimum and
maximum-density maximal independent sets are hard optimization problems. In
this paper, we use cavity method of statistical physics and Monte Carlo
simulations to study the corresponding constraint satisfaction problem on
random graphs. We obtain the entropy of maximal independent sets within the
replica symmetric and one-step replica symmetry breaking frameworks, shedding
light on the metric structure of the landscape of solutions and suggesting a
class of possible algorithms. This is of particular relevance for the
application to the study of strategic interactions in social and economic
networks, where maximal independent sets correspond to pure Nash equilibria of
a graphical game of public goods allocation
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